Reliable estimates of volatility and correlation are fundamental in economics and finance for understanding the impact of macroeconomics events on the market and guiding future investments and policies. Dependence across financial returns is likely to be subject to sudden structural changes, especially in correspondence with major global events, such as the COVID-19 pandemic. In this work, we are interested in capturing abrupt changes over time in the dependence across US industry stock portfolios, over a time horizon that covers the COVID-19 pandemic. The selected stocks give a comprehensive picture of the US stock market. To this end, we develop a Bayesian multivariate stochastic volatility model based on a time-varying sequence of graphs capturing the evolution of the dependence structure. The model builds on the Gaussian graphical models and the random change points literature. In particular, we treat the number, the position of change points, and the graphs as object of posterior inference, allowing for sparsity in graph recovery and change point detection. The high dimension of the parameter space poses complex computational challenges. However, the model admits a hidden Markov model formulation. This leads to the development of an efficient computational strategy, based on a combination of sequential Monte-Carlo and Markov chain Monte-Carlo techniques. Model and computational development are widely applicable, beyond the scope of the application of interest in this work.

中文翻译：

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动态高斯图模型中的变化点检测：COVID-19 大流行对美国股市的影响

对波动性和相关性的可靠估计是经济学和金融学的基础，有助于了解宏观经济事件对市场的影响并指导未来的投资和政策。对财务回报的依赖可能会受到突然的结构性变化的影响，尤其是在应对重大全球事件时，例如 COVID-19 大流行。在这项工作中，我们有兴趣在涵盖 COVID-19 大流行的时间范围内捕捉美国行业股票投资组合的依赖性随时间的突然变化。所选股票全面反映了美国股市。为此，我们开发了一个贝叶斯多元随机波动率模型，该模型基于捕获依赖结构演变的时变图序列。该模型建立在高斯图形模型和随机变化点文献之上。特别是，我们将变化点的数量、位置和图形视为后验推断的对象，从而允许图形恢复和变化点检测中的稀疏性。参数空间的高维带来了复杂的计算挑战。然而，该模型承认一个隐藏的马尔可夫模型公式。这导致了基于顺序蒙特卡洛和马尔可夫链蒙特卡洛技术组合的有效计算策略的发展。模型和计算开发广泛适用，超出了本工作感兴趣的应用范围。允许图恢复和变化点检测中的稀疏性。参数空间的高维带来了复杂的计算挑战。然而，该模型承认一个隐藏的马尔可夫模型公式。这导致了基于顺序蒙特卡洛和马尔可夫链蒙特卡洛技术组合的有效计算策略的发展。模型和计算开发广泛适用，超出了本工作感兴趣的应用范围。允许图恢复和变化点检测中的稀疏性。参数空间的高维带来了复杂的计算挑战。然而，该模型承认一个隐藏的马尔可夫模型公式。这导致了基于顺序蒙特卡洛和马尔可夫链蒙特卡洛技术组合的有效计算策略的发展。模型和计算开发广泛适用，超出了本工作感兴趣的应用范围。